A signal processing system may perform operations that involve transforming a signal from one domain to another through the use of the Fourier transform or some other suitable transform. Implementations of the Fourier transform, such as the fast Fourier transform (“FFT”), the inverse FFT (“IFFT”), the discrete Fourier transform (“DFT”), and the inverse DFT (“IDFT”), are used in a wide variety of applications and devices. As one example, a communication system may employ the DFT to transform a time domain signal to a frequency domain signal to perform noise reduction operations in the frequency domain and then employ the IDFT to transform the resulting signal back to the time domain.
In practice, transformation operations may consume a relatively large amount of power and/or processing resources. For example, in some applications FFT, IFFT, DFT, or IDFT operations may be computationally intensive in that they may involve a relatively large number of multiply and accumulate operations per second. Consequently, a processor that performs these operations may consume a significant amount of power. This power consumption problem may be exacerbated in high data rate applications, where the processor that performs transform operations may be one of the main sources of power consumption in a system. Also, in some applications an analog signal may be converted to a digital signal and digital signal processing may be employed to transform the digital signal from one domain to another. In such a case, the frequency conversion, analog-to-digital (ND) conversion before processing, and digital-to-analog (D/A) conversion after processing results in additional power consumption. For some applications (e.g., portable wireless devices, sensors, space-borne systems, and other applications that involve the processing of high speed signals but where available power may be limited), the use of such transform techniques may be problematic due to the high power consumption.
Moreover, conventional techniques for implementing the FFT, DFT, or IDFT may employ a relatively large number of elements that occupy a large area and that have a large number of interconnections. These factors may result in significant signal propagation or processing delays in some cases. Additionally, conventional techniques may store partial products and coefficients in memory during transform operations, which may increase hardware complexity.
In view of the above, conventional transform techniques may be difficult to implement at high data rates (e.g., microwave frequencies) and may have poor performance at these frequencies. Consequently, a need exists for more effective techniques for transforming signals.
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